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One needs to understand
the theory behind

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the hypothesis testing and how do

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you reject a null
hypothesis or otherwise.

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There are rules of thumb.

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That is in case of
a two-tail test,

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one can use 1.96 as the
calculated threshold for

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either Z or T statistics to reject

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a null hypothesis or
for a one-tail test,

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absolute value of 1.64 to
reject a null hypothesis.

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But what does it mean,

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how do you get to
these 1.64 or 1.96?

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There is some theory to it.

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It involves statistical
distributions and

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now perhaps is a good time to,

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to learn about those.

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Now imagine if the mean values

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of two variables is the same.

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That is, we are assuming
that the difference

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between the two means
is essentially zero.

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Let's say the mean of

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variable A and the
mean of Variable B,

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we assume that they are equal,

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that is mu_A equals mu_B.

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And if that were to be the case,

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the difference between the
two should be equal to zero.

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So the alternative
hypothesis could

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be that the differences
mean is not equal to zero.

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So, and you would say that
mu_A is not equal to mu_B,

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or the difference is
greater than zero.

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That is, mu_A is
greater than mu_B,

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or the difference
is less than zero,

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where mu_A is less than mu_B.

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And in these three circumstances,

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the rejection region
or the how do

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you reject the null hypothesis

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means three different things.

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And for this, we were to revert

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to the normal distribution curve.

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Imagine that you're
conducting a Z-test using

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a normal distribution and

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the shape of the curve
would be very similar.

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This image will be very
similar if we were to do

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a two-tailed test
for T-distribution.

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But let's assume that
we are working with

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normal distribution and you
have a rejection region

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that is to the left and to
the right of the curve,

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as you saw the normal
distribution curve.

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Let's say our alternative
hypothesis is

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that the mean difference
is not equal to zero.

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It could be greater
than or less than zero,

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but it's not equal to zero.

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So we will call this a two-tail
test because we are not

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making an assumption of

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the difference being
greater or less than zero.

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Then we have to define

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the rejection region
in both tails,

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that is the left tail and

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the right tail of the
normal distribution.

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Remember we only consider 5
percent of the area under

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the normal curve to define
the rejection region

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and for the two-tail tests
that 5 percent gets divided

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into half of it goes into

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the left tail and the other half

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goes into the right tail,

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so two and half percent under
the curve in each tail.

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Graphically you can see this

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again as the same
as we saw earlier,

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that this is a normal
distribution curve

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and two-and-a-half percent is

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in the left tailed into the other

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two-and-a-half percent
is in the right tail.

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If the test statistic is 1.96,

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if the absolute value of

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the test statistic is greater

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than 1.96 or less than 1.96,

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it falls in the rejection region

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and you can safely
reject the null.

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The null would be that the
difference of mean equals to

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zero or in common parlance,

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what we are saying is

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that the two means
are not the same.

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Now let us work with the
assumption of the situation

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where we're testing if

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the difference of mean
is less than zero,

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we are only interested
in the left tail.

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Our alternative hypothesis is

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that the difference of
mean is less than zero.

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In this case, the entire
rejection region,

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that is 5 percent of
the rejection region is

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to the left and in
any situation in,

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for a one-tailed test,

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if we were to get the
T-stat of 1.64 or less,

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we would reject the null that
the mean is greater than

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zero in favor of

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the alternative that the
difference is less than zero.

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The exact opposite to

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this would be the
right tailed test.

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Where the alternative
hypothesis is

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that the mean is
greater than zero.

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And if you get the
T-test statistics

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of greater than 1.64,

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for a right-tailed test,

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you reject the null in favor
of the alternative that

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the mean difference
is greater than zero.